The Related Fluid Development Equations Research On Regularity Criterion And Vanishing Viscosity Limit

The Navier-Stokes equation is used to study viscous incompressible fluids and is a classic model of viscous incompressible fluids.In fluid mechanics,the model of coupling the Navier-Stokes equation with other equations has important research value.This thesis mainly studies two types of fluids Regularity criterion and inviscidity limit of mechanical equations.The research content is divided into the following two parts.The first part mainly studies the regularity criterion of Navier-Stokes-Cahn-Hilliard system in Morrey-Campanato space.Using energy estimation,Gagliardo-Nirenberg inequality,embedding theorem and the properties of MC space,the overall prior estimation is obtained,and then we get The regularity of the overall solution of the system.In the second part,we mainly study the existence,uniqueness and vanishing viscosity limit of the global strong solution of a new magnetohydrodynamic system in two dimensions.First,based on the energy estimation,the evolution of the Stokes equation and the basic inequality prove that the equation has a global Strong solution and uniqueness of strong solution.Secondly,under the assumption of strong solution of the equation,using basic inequality and Gronwall inequality,when the viscosity coefficient tends to 0,in the sense of L~2norm,the solution of the MHD equation with viscosity coefficient Approximate the solution of an equation without viscosity coefficients.